Problem

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: number theory



Find all sets $(a, b, c)$ of different positive integers $a$, $b$, $c$, for which: * $2a - 1$ is a multiple of $b$; * $2b - 1$ is a multiple of $c$; * $2c - 1$ is a multiple of $a$.